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The matrix $A = (\begin{array}{cc} p & - q \\ q & p \end{array})$ is orthogonal if and only if

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p2 + q2 = 1

p2=q2

p2=q2+1

none of these

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detailed solution

Correct option is A

AA′=I⇒p−qqppq−qp=1001⇒p2+q200p2+q2=1001∴p2+q2=1

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The matrix A=p−qqp is orthogonal if and only if

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The matrix $A = (\begin{array}{cc} p & - q \\ q & p \end{array})$ is orthogonal if and only if